Operator Theory, 8.0 credits
Operator Theory, 8.0 hp
6FMAI09
Course level
Third-cycle EducationDescription
Contact the examiner if interested.
Current and recently held PhD courses at the Department of Mathematics can be found here: https://liu.se/artikel/doktorandkurser-vid-matematiska-institutionen
Contact
-
Evgeniy Lokharu
Examiner
Entry requirements
The course requires some basic knowledge from Functional Analysis (Normed spaces, Bounded operators and Functionals).
Contents
This course covers selected topics of spectral theory of linear operators in Hilbert and Banach spaces. A special attention will be paid to examples and applications. The following topics are included:
- Bounded linear operators in Hilbert and Banach spaces.
- Spectrum and Resolvent.
- Compacts operators.
- Fredholm operators.
- Fredholm Alternative.
- Self-Adjont operators.
Educational methods
Lectures and problem solving seminars.
Examination
Exercises (assignments).
Grading
Two-grade scaleCourse literature
Course literature: M. Reed, B. Simon, ”Methods Of Modern Mathematical Physics”, Vol.1, Academic Press, 1981.
Supplementary literature: E. Kreyszig, ”Introductory Functional Analysis with Applications”, Wiley, 1989.